I'll play Devil's Advocate here.
Arrows are hard to use in aerial attacks. Flying mounts make for very unstable platforms, and wind is much more of an issue even a few hundred feet up. Also, the archer must take into consideration not only the target's motion, but the mount's. A defender on the ground has an advantage--he or she only needs to account for the flying range & speed, and has a stable surface from which to fire.
Swords & lances come into their own in dogfights & fly-by attacks. In the former, you may be able to leap from one mount to another, or successfully drive off an attacker that would otherwise easily strike the mount, and close-range weaponry is essential here. For a fly-by, you only need to hit once. Indeed, you only have time to make one attack, so you had better make it count. The mount may be easier to train for this, as it doesn't need to actually go in for an attack, just get close. Fly in fast & tight, with the wings held closely to the body.
The chief difference is that it cannot really be a stand-up attack sequence. It's mostly about manoeuvring. You do many aerial acrobatics and maybe, just maybe, get in one shot.
I like the smaller flying critters idea. Augmenting that is chaff, or just debris thrown behind the flyers. Getting streamers in your face & wings, or just a bunch of nails or something, can mean the difference between winning and crashing.